Thread: arithmetic progression

Hiya, I was just having some trouble with this qn.

An AP has first term 75 and nth term -72. Sum of its first n terms is 33. Find n(i got 22-and i'm sure it's right-check if you might). Given that the sum from the (k+1)th term to the (2k)th term of the progression is positive, find k's greatest value.

(Ans:7 but how to get it?) Anyway thx a mil to whoever set up this forum...it's great! :P

Originally Posted by zeromeyzl

Hiya, I was just having some trouble with this qn.

An AP has first term 75 and nth term -72. Sum of its first n terms is 33. Find n(i got 22-and i'm sure it's right-check if you might). Given that the sum from the (k+1)th term to the (2k)th term of the progression is positive, find k's greatest value.

(Ans:7 but how to get it?) Anyway thx a mil to whoever set up this forum...it's great! :P

n = 22 is correct.

Then -72 = 75 + 21d => d = -2.

So the first term is 75 and the common difference is -2. Therefore .

Therefore:




.


So solve for the largest integer value of k.

I get k = 25.